Russell's hypersurface from a geometric point of view

TL;DR

This paper presents a new geometric proof of Makar-Limanov's theorem, demonstrating that Russell's hypersurface cannot be isomorphic to affine three-space, thereby deepening understanding of its geometric properties.

Contribution

It provides a novel geometric perspective and proof of the non-isomorphism of Russell's hypersurface to affine space, expanding the theoretical understanding.

Findings

Russell's hypersurface is not isomorphic to affine three-space

New geometric proof of Makar-Limanov's theorem

Enhanced understanding of hypersurface properties

Abstract

We give a new proof of Makar-Limanov's theorem, which states that Russell's hypersurface is not isomorphic to affine three space.